NOTES ON ORTHOGONAL ALMOST COMPLEX STRUCTURES ON THE RIEMANNIAN PRODUCTS

초록

In this paper, we show that there does not exist an orthogonal almost complex structure on a Riemannian product of a compact Riemann surface with negative constant curvature and a round 4-sphere. In addition, we prove that any orthogonal almost complex structure on a Riemannian product of a compact Riemann surface with negative constant curvature and a round 6-sphere is never integrable. © 2025 Pushpa Publishing House, Prayagraj, India.

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